Projections Onto Order Simplexes and Isotonic Regression.

Isotonic regression is the problem of fitting data to order constraints. This problem can be solved numerically in an efficient way by successive projections onto order simplex constraints. An algorithm for solving the isotonic regression using successive projections onto order simplex constraints was originally suggested and analyzed by Grotzinger and Witzgall. This algorithm has been employed repeatedly in a wide variety of applications. In this paper we briefly discuss the isotonic regression problem and its solution by the Grotzinger-Witzgall method. We demonstrate that this algorithm can be appropriately modified to run on a parallel computer with substantial speed-up. Finally we illustrate how it can be used to pre-process mass spectral data for automatic high throughput analysis.